On the Pareto-Optimal Beam Structure and Design for Multi-User MIMO Interference Channels

TL;DR

This paper investigates the structure of Pareto-optimal beams in multi-user MIMO interference channels, proposing a new parameterization and efficient design algorithm that reduce complexity, especially for massive MIMO systems.

Contribution

It introduces a necessary condition for Pareto-optimal covariance matrices and develops a geometrically efficient beam design method based on manifold optimization.

Findings

The proposed parameterization reduces search space and computational complexity.

Numerical results validate the effectiveness of the beam design method.

The approach is particularly beneficial for massive MIMO systems.

Abstract

In this paper, the Pareto-optimal beam structure for multi-user multiple-input multiple-output (MIMO) interference channels is investigated and a necessary condition for any Pareto-optimal transmit signal covariance matrix is presented for the K-pair Gaussian (N,M_1,...,M_K) interference channel. It is shown that any Pareto-optimal transmit signal covariance matrix at a transmitter should have its column space contained in the union of the eigen-spaces of the channel matrices from the transmitter to all receivers. Based on this necessary condition, an efficient parameterization for the beam search space is proposed. The proposed parameterization is given by the product manifold of a Stiefel manifold and a subset of a hyperplane and enables us to construct a very efficient beam design algorithm by exploiting its rich geometrical structure and existing tools for optimization on Stiefel manifolds. Reduction in the beam search space dimension and computational complexity by the proposed parameterization and the proposed beam design approach is significant when the number of transmit antennas is larger than the sum of the numbers of receive antennas, as in upcoming cellular networks adopting massive MIMO technologies. Numerical results validate the proposed parameterization and the proposed cooperative beam design method based on the parameterization for MIMO interference channels.